Factor Trees

Find a number that will divide exactly (divisible) into the number being factored (see Divisibility Tests.) It doesn't really matter which number you pick. The same prime factorization results. The number you think of first will probably get the quickest results. Don't spend five minutes looking for a shortcut which will save you three.

Keep breaking up the resulting factors until all results are prime.

Copy all prime factors down to each successive level so that each level multiplies up to the original number. This will cut down on mistakes and ensure that all factors will be available for calculating greatest common factors (GCFs) and least common multiples (LCMs) or least common denominators (LCDs).

In general, the closer two divisors are in value to each other, the shorter the factor tree will be.


Shortcuts worth memorizing: 

  8=23      12=22.3      10n=2n.5n
Examples: 

      12     or    12                  60       or      60       or       60
     / \          / \                /    \            / \              /  \
    4 . 3         2 . 6             6   .  10         12 . 5            2 . 30
   / \   \      /   / \           / \    / \        / \   \           /   / \
  2 . 2 . 3     2 . 2 . 3          2 . 3 . 2 . 5      4 . 3 . 5          2 . 6 . 5
                                                  / \   \   \        /   / \   \
     22.3          22.3                22.3.5       2 . 2 . 3 . 5      2 . 2 . 3 . 5

                                                     22.3.5             22.3.5


         96       or      96                   5760                 96,000,000
        /   \            /  \                 /    \               /  \   \   \
      8   .  12         8 . 12              60   .  96            8 . 12 . 26 . 56
     / \    / \       /      \            /  \    /  \          /     |    \    \
    2 . 4 . 4 . 3     23  .  22.3          6 . 10 . 8 . 12        23 . 22.3 . 26 . 56
   /   /|   |\   \                       /|   |\   \    \
  2 . 2.2 . 2.2 . 3      2 5.3           2.3 . 2.5 . 23 . 22.3          210.3.56

        25.3                                  27.32.5
Last updated 10/24/97 - 5/8/2000.

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